The Problem of Induction

Core Idea

Hume showed that inductive inference—concluding universal laws from repeated observations—cannot be logically justified. The fact that the sun has risen every day in the past does not logically guarantee it will tomorrow. This challenge remains central to philosophy of science because all empirical science relies on generalizing from observed instances to universal claims.

How It's Best Learned

Start with Hume's original problem formulation. Then study Popper's falsificationist response and modern Bayesian approaches to see the landscape of proposed solutions.

Common Misconceptions

Thinking induction is illogical (Hume allows practical induction, just denies its theoretical justification). Confusing induction with deduction. Assuming the problem is purely logical rather than epistemological.

Explainer

You already understand inductive reasoning: it is the move from particular observations to general conclusions. The sun has risen every day in recorded history, so we conclude it will rise tomorrow. Every copper sample we have tested conducts electricity, so we generalize that copper is electrically conductive. Science depends on this pattern constantly. Hume's devastating observation was simple: this inference is never deductively valid. The premises — all the past sunrises — do not *guarantee* the conclusion. The future could, as far as logic is concerned, deviate from the past in any way whatsoever. No number of observed instances logically compels the universal conclusion.

The deeper problem is that attempts to justify induction seem to require using induction itself. Why do we trust that the future will resemble the past? The most natural answer is: "Because in the past, the future has always resembled the past." But this is precisely the kind of inductive argument whose validity is in question. Any defense of induction that appeals to past success of induction is viciously circular. Hume concluded that our habit of inductive inference is psychologically irresistible — custom and habit, not rational justification — and that we cannot provide a non-circular philosophical foundation for it.

This cuts to the heart of science. From empiricism you know that scientific knowledge is grounded in observation and experiment. But observations give us particular facts; scientific laws are universal claims. Every generalization in science — Newton's laws, the laws of thermodynamics, evolutionary theory — makes a claim that goes beyond the finite observations supporting it. If induction cannot be rationally justified, how can science claim to produce genuine knowledge rather than merely well-confirmed belief? Hume's problem is not a logical puzzle to be solved and set aside; it is an open wound in the foundations of empirical knowledge.

Karl Popper's response — which you will study in falsificationism — was to abandon justification entirely. We cannot verify universal laws, but we can falsify them: a single contrary observation logically refutes the universal claim. Science proceeds not by accumulating confirming instances but by making bold conjectures and subjecting them to rigorous attempts at refutation. The Bayesian response takes a different route: rather than demanding logical certainty, it replaces the demand for justification with a probabilistic framework. Prior credences are updated by evidence using Bayes' theorem, and "justified" comes to mean having high posterior probability given the evidence. Neither solution fully dissolves Hume's challenge — Popper does not explain why we should act on unfalsified theories, and Bayesianism must still assume that past evidence is relevant to future credences — but they represent the two most influential frameworks for living with the problem rather than solving it.